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arxiv: 2606.29990 · v1 · pith:ZI3ZXFXQnew · submitted 2026-06-29 · 🌌 astro-ph.SR

Multi-height Identification of Sausage and Fluting Eigenmodes in a Solar Pore

Shahin Jafarzadeh , David B. Jess , Marco Stangalini , Luiz A. C. A. Schiavo , Timothy J. Duckenfield , Suzana S. A. Silva , Gary Verth , Viktor Fedun
show 29 more authors
Sami K. Solanki H. N. Smitha Andreas Lagg Achim Gandorfer Alex Feller Francisco A. Iglesias Tino L. Riethm\"uller Bianca Grauf Johannes Hoelken Yukio Katsukawa Pietro Bernasconi Thomas Berkefeld Alberto \'Alvarez-Herrero Masahito Kubo David Orozco Su\'arez Michael Carpenter Alexander Bell Valent\'in Mart\'inez Pillet Francisco Javier Bail\'en Julian Blanco Rodr\'iguez Juan Sebasti\'an Castellanos Dur\'an Edvarda Harnes Ryohtaroh T. Ishikawa Yusuke Kawabata Takuma Matsumoto Takayoshi Oba Azaymi L. Siu-Tapia Hanna Strecker Du\v{s}an Vukadinovi\'c
This is my paper

Pith reviewed 2026-06-30 04:20 UTC · model grok-4.3

classification 🌌 astro-ph.SR
keywords solar poresMHD wavessausage modesfluting modesproper orthogonal decompositionsolar photospherewave propagationchromosphere
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The pith

Multi-height observations identify sausage modes as standing and fluting modes as upward propagating in a solar pore.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper applies proper orthogonal decomposition to pore-boundary oscillations extracted from eight spectral lines that sample different formation heights over roughly 500 km. The first mode in every line is an axisymmetric sausage mode carrying most of the power at 1-2 mHz, while the second mode is a fluting mode with azimuthal wave number 2 at 2-3.5 mHz. Wavelet phase analysis of the temporal coefficients shows near-zero phase difference with height for the sausage mode and a systematic phase increase reaching about 50 degrees for the fluting mode. A reader cares because this supplies the first direct multi-height characterisation of the vertical structure of these eigenmodes inside a compact magnetic waveguide.

Core claim

In all eight lines the first POD mode is consistently an axisymmetric sausage mode with dominant power at approximately 1-2 mHz that carries 66-86 percent of the normalised eigenvalue fraction, while the second mode is a fluting mode with m=2 dominant at 2-3.5 mHz that contributes 4-10 percent. Cross-line wavelet phase analysis shows the sausage mode remains close to zero phase difference across the sampled heights, consistent with standing or near-standing behaviour, whereas the fluting mode displays a modest but systematic increase in phase with height reaching about 50 degrees, indicative of an upward-propagating component.

What carries the argument

Proper orthogonal decomposition applied to the time series of pore-boundary positions identified in each of eight spectral lines.

If this is right

  • The sausage mode dominates oscillation power and behaves as a standing wave across the photosphere to low chromosphere.
  • The fluting mode carries a propagating component capable of transporting energy upward.
  • Mode identification remains consistent regardless of the exact height sampled within the 500 km range.
  • Lower-frequency power concentrates in the sausage mode while higher frequencies appear in the fluting mode.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same boundary-tracking and decomposition approach could be used on other compact magnetic structures to separate standing from propagating wave energy.
  • The clear frequency separation between the two modes suggests they may be excited by different photospheric drivers.
  • Because the sausage mode shows little net phase progression, it is unlikely to carry significant time-averaged energy flux through the pore.

Load-bearing premise

The eight spectral lines correspond to distinct formation heights that increase systematically across roughly 500 km.

What would settle it

If POD applied to boundary oscillations in a new pore or with a different set of lines yields a different ordering of modes or if the fluting-mode phase difference shows no systematic increase with height.

Figures

Figures reproduced from arXiv: 2606.29990 by Achim Gandorfer, Alberto \'Alvarez-Herrero, Alexander Bell, Alex Feller, Andreas Lagg, Azaymi L. Siu-Tapia, Bianca Grauf, David B. Jess, David Orozco Su\'arez, Du\v{s}an Vukadinovi\'c, Edvarda Harnes, Francisco A. Iglesias, Francisco Javier Bail\'en, Gary Verth, Hanna Strecker, H. N. Smitha, Johannes Hoelken, Juan Sebasti\'an Castellanos Dur\'an, Julian Blanco Rodr\'iguez, Luiz A. C. A. Schiavo, Marco Stangalini, Masahito Kubo, Michael Carpenter, Pietro Bernasconi, Ryohtaroh T. Ishikawa, Sami K. Solanki, Shahin Jafarzadeh, Suzana S. A. Silva, Takayoshi Oba, Takuma Matsumoto, Thomas Berkefeld, Timothy J. Duckenfield, Tino L. Riethm\"uller, Valent\'in Mart\'inez Pillet, Viktor Fedun, Yukio Katsukawa, Yusuke Kawabata.

Figure 1
Figure 1. Figure 1: Observational context and selected spectral lines used in the present analysis. The left panel shows a SUSI slit-jaw image near the continuum. The yellow lines mark the full raster field of view, while the dashed blue rectangle marks the smaller portion of that field shown in the middle panel. The arrow and green contour indicate the pore analysed in this work. The middle panel presents representative line… view at source ↗
Figure 2
Figure 2. Figure 2: Two dominant recovered POD modes identified from the pore-boundary oscillations in the eight selected spectral lines, ordered by increasing formation height from bottom to top. For each line, the first three columns show the first recovered POD mode and the last three columns the second recovered POD mode. Within each group, the panels show the spatial eigenfunction, the corresponding temporal coefficient,… view at source ↗
Figure 3
Figure 3. Figure 3: Consensus phase behaviour of the two dominant recovered POD modes across the selected spectral lines. The phase is measured relative to the lowest-forming selected line, Fe ii 327.6617 nm, and is shown for the frequency bands in which the common coherence is strongest: 1.5 ± 0.3 mHz for the sausage mode and 3.2 ± 0.3 mHz for the fluting mode. Only phase values from regions outside the cone of influence and… view at source ↗
read the original abstract

Magnetic pores are compact, strongly magnetised waveguides in the lower solar atmosphere and therefore provide favourable conditions for identifying magnetohydrodynamic (MHD) wave modes. Earlier seeing-free observations revealed concurrent sausage, kink, and fluting modes in photospheric pores, but only at a single sampled layer. In this Letter, we exploit the dense spectral sampling of the near-ultraviolet 327-329 nm window observed by the Sunrise-III UV Spectropolarimeter and Imager (SUSI) to investigate how pore wave modes behave across multiple photospheric and low-chromospheric heights spanning roughly 500 km. We analyse ~75 min of a Sunrise-III/SUSI time series containing a small solar pore. From eight selected spectral lines sampling different estimated formation heights, we identify the pore boundary at each line and time step and apply proper orthogonal decomposition (POD) to the boundary oscillations. In all eight lines, the first POD mode is consistently identified as an axisymmetric sausage mode, with dominant power at ~1-2 mHz, and carries the dominant normalised eigenvalue fraction, typically about 66-86%, while the second mode is a fluting mode with azimuthal wave number m = 2, dominant at ~2-3.5 mHz, and contributes about 4-10%. Cross-line wavelet phase analysis of the temporal coefficients shows that the sausage mode remains close to zero phase difference across the sampled heights, consistent with standing or near-standing behaviour, whereas the fluting mode displays a modest but systematic increase in phase with height, reaching about 50 degrees, indicative of an upward-propagating component. These observations provide the first multi-height identification and phase characterisation of sausage and fluting modes inferred from pore-boundary oscillations.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 2 minor

Summary. The paper reports the first multi-height identification of sausage (m=0) and fluting (m=2) MHD eigenmodes in a solar pore using proper orthogonal decomposition (POD) applied to pore-boundary oscillations extracted from eight spectral lines in the 327-329 nm window observed by Sunrise-III/SUSI. Across all lines, the dominant POD mode is identified as sausage with power at 1-2 mHz (66-86% eigenvalue fraction) and the second as fluting at 2-3.5 mHz (4-10%); wavelet phase analysis of temporal coefficients shows near-zero phase difference (standing behavior) for sausage and a systematic ~50° increase with height (upward propagation) for fluting over an estimated ~500 km height range.

Significance. If the formation-height ordering holds, the work supplies the first observational constraints on the vertical structure and propagation character of these modes across the photosphere-low chromosphere transition in a pore waveguide. The consistency of mode identification across eight independent lines and the direct extraction of frequencies and phase differences from the data (no fitted parameters) are strengths that would advance wave-mode diagnostics in solar magnetic structures.

major comments (1)
  1. [Section describing spectral-line selection and height assignment (near the multi-height analysis)] The central interpretation of the fluting-mode phase gradient as evidence of upward propagation rests on the eight lines providing distinct, correctly ordered formation heights spanning ~500 km. The manuscript states these heights are 'estimated' from the 327-329 nm window but provides no contribution-function calculations, model-atmosphere comparisons, or other independent validation of the ordering and separation; any overlap or misordering would render the cross-line wavelet phase vs. height trend uninterpretable.
minor comments (2)
  1. [POD mode identification subsection] Clarify the precise criterion used to assign azimuthal wavenumber m=2 to the second POD mode (e.g., spatial structure of the eigenfunction or additional diagnostics).
  2. [Results section] The normalized eigenvalue fractions (66-86% and 4-10%) are reported per line; a table summarizing these values across all eight lines would improve readability.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the thorough review and for highlighting the importance of validating the formation-height ordering. We address the single major comment below and will revise the manuscript accordingly to strengthen the multi-height interpretation.

read point-by-point responses

  1. Referee: The central interpretation of the fluting-mode phase gradient as evidence of upward propagation rests on the eight lines providing distinct, correctly ordered formation heights spanning ~500 km. The manuscript states these heights are 'estimated' from the 327-329 nm window but provides no contribution-function calculations, model-atmosphere comparisons, or other independent validation of the ordering and separation; any overlap or misordering would render the cross-line wavelet phase vs. height trend uninterpretable.

    Authors: We agree that the current manuscript describes the heights as estimated without supplying explicit contribution-function calculations or new model-atmosphere comparisons. The line selection and approximate ordering draw on established formation-height ranges for the 327-329 nm window reported in prior SUSI and UV spectroscopy studies, but these references are not detailed in the text. To address the concern directly, we will revise the manuscript by adding a concise subsection (or expanded methods paragraph) that cites the relevant literature on line-formation heights in this spectral region and notes the expected photospheric-to-low-chromospheric progression. This addition will supply the independent validation requested and allow readers to evaluate the robustness of the ordering. We do not claim the revision eliminates all uncertainty in absolute heights, but it will make the basis for the relative ordering explicit. revision: yes

Circularity Check

0 steps flagged

No circularity: pure observational extraction from time series

full rationale

The paper performs direct data analysis on observed time series from eight spectral lines: boundary identification, POD decomposition of oscillations, frequency power spectra, eigenvalue fractions, and cross-line wavelet phase differences. All reported quantities (1-2 mHz sausage dominance at 66-86%, 2-3.5 mHz fluting at 4-10%, ~50° phase gradient) are computed outputs from the input data and standard methods (POD, wavelets). No step reduces a claimed prediction or eigenmode identification to a fitted parameter defined from the same data, nor relies on self-citation chains for uniqueness or ansatz. Formation-height estimates are external inputs from literature/models, not internally derived quantities renamed as results. The derivation chain is therefore self-contained and non-circular.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on standard mathematical properties of POD and wavelet analysis plus domain assumptions about spectral-line formation heights and the correspondence between boundary oscillations and MHD eigenmodes; no free parameters are fitted to produce the reported frequencies or phases, and no new physical entities are introduced.

axioms (2)
  • domain assumption Proper orthogonal decomposition applied to pore-boundary time series separates axisymmetric sausage and m=2 fluting eigenmodes.
    The paper interprets the first two POD modes as sausage and fluting on the basis of symmetry and azimuthal wavenumber.
  • domain assumption The eight spectral lines form at sufficiently separated heights to permit meaningful cross-line phase comparison.
    The multi-height analysis depends on the estimated formation heights stated in the abstract.

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